Liquid-vapor oscillations of water in hydrophobic nanopores

Abstract

Water plays a key role in biological membrane transport. In ion channels and water-conducting pores (aquaporins), one-dimensional confinement in conjunction with strong surface effects changes the physical behavior of water. In molecular dynamics simulations of water in short (0.8 nm) hydrophobic pores the water density in the pore fluctuates on a nanosecond time scale. In long simulations (460 ns in total) at pore radii ranging from 0.35 to 1.0 nm we quantify the kinetics of oscillations between a liquid-filled and a vapor-filled pore. This behavior can be explained as capillary evaporation alternating with capillary condensation, driven by pressure fluctuations in the water outside the pore. The free-energy difference between the two states depends linearly on the radius. The free-energy landscape shows how a metastable liquid state gradually develops with increasing radius. For radii > approximately 0.55 nm it becomes the globally stable state and the vapor state vanishes. One-dimensional confinement affects the dynamic behavior of the water molecules and increases the self diffusion by a factor of 2-3 compared with bulk water. Permeabilities for the narrow pores are of the same order of magnitude as for biological water pores. Water flow is not continuous but occurs in bursts. Our results suggest that simulations aimed at collective phenomena such as hydrophobic effects may require simulation times >50 ns. For water in confined geometries, it is not possible to extrapolate from bulk or short time behavior to longer time scales.

Fig. 1.

(a) Oscillating water density in model pores of increasing pore radius R. The water density n(t) (in units of the bulk water density n_bulk) over the simulation time shows strong fluctuations on a greater than ns time scale (50-ps moving average smoothing). Two distinctive states are visible: open at approximately n_bulk (liquid water) and closed with very little or no water in the pore (water vapor). (b) The pore model consists of methane pseudo atoms of van der Waals radius 0.195 nm. A water molecule is drawn to scale. (c) Permeant water molecules in a R = 0.55-nm pore as it switches from the open to the closed state. Z-coordinates of the water oxygen atoms are drawn every 2 ps. The mouth and pore region are indicated by horizontal broken and solid lines. Five trajectories are shown explicitly. The white water molecule permeates the pore within 54 ps, whereas the black one requires only ≈10 ps.

Fig. 2.

Water density in hydrophobic pores with radii ranging from 1 to 0.4 nm. (Left) Density z-averaged over the length of the pore. (Right) Radially averaged density. The density is in units of SPC bulk water at 300 K and 1 bar [plots were prepared with xfarbe 2.5 (32)].

Fig. 3.

(a) Openness 〈ω(R)〉 of hydrophobic pores and free-energy difference ΔF(R) between states (Inset). Wide pores are permanently water-filled (〈ω〉 = 1), whereas narrow ones are predominantly empty (〈ω〉≈ 0). The broken line is the function (1 + exp[-βΔF_eq(R)])^-1, with ΔF_eq(R) determined independently of 〈ω(R)〉. ΔF(R) appears to be a linear function of R, regardless of whether it is estimated from the kinetics (ΔF_kin) or the equilibrium probability distribution of the pore occupancy (ΔF_eq). (b) Radial potential of mean force of water F(r). Very narrow pores show a relatively featureless PMF, consistent with a predominantly vapor-like state. For larger pore radii, the liquid state dominates. The PMF of the 1-nm pore is very similar to the one of water near a planar hydrophobic slab (R = ∞). PMFs are drawn with arbitrary offsets. (c) Kinetics open ⇌ closed. The average lifetime of the open-state τ_o depends on the radius exponentially, whereas τ_c is approximately constant in the two-state region (compare to Fig. 4) of radii.

Fig. 4.

(a) Free-energy density f(T, n) at constant T = 300 K. (b) Chemical potential μ(T, n). n is the water density in the pore, normalized to n_bulk = 53.7 mol·liter^-1. f is given in units of k_BT and the inverse of the liquid molecular volume of bulk water (). Two minima correspond to the observed two-state behavior. The vapor state becomes metastable with increasing radius, and for R > 0.55 nm the liquid state is globally stable. f(T, n; R = 1.0 nm) is drawn with an arbitrary offset.